Nonparametric Optimization with Objective Operational Statistics
- Author(s): Yu, Lian
- Advisor(s): Lim, Andrew E.B.
- et al.
In the first part of this thesis, we study the non-parametric
methods for estimation and optimization. In particular, a new
non-parametric method, objective operational statistics, is proposed
to inventory control problems, where the only information available
is the sample data and we do not assume any relationship between
demands and order quantities. A kernel algorithm based on objective
operational statistics is constructed to approximate the objective
function directly from sample data. Moreover, we give conditions
under which the operational statistics approximation function
converges to the true objective. Numerical results of the algorithm
with applications to newsvendor problem show that the objective
operational statistics approach works well for small amount of data
and outperforms the previous parametric and non-parametric methods.
In the second part of this thesis, we present a robust hedging
problem under model uncertainty and the bounds of the optimal
objective value are derived by duality analysis.